Smoke and Resolve are in fact two very different programs. While i don't know Resolve very well and haven't used its editorial features, I do know Smoke very well and it is my main tool.
Smoke is a fully fledged post production tool with advanced visual effects / finishing capabilities. It has not just editorial features, but color correction, roto, masking, special effects filters, keying, and an advanced node-based compositing toolset.
Resolve is primarily a color correction tool... an advanced one though, and it probably does a better job with color correction than Smoke does, even though Smoke's color tools are nice... but Resolve probably shines better when color correcting. I have heard of people having two different login environments, one for Smoke and another for Resolve. They conform and color correct in Resolve, then bring that timeline into Smoke to finish.
Autodesk has an excellent academic program, and as you have stated, their software for education is free, after a relatively painless registration process. It woudn't hurt to try it out. You could also check into their other software, since you'll already be registered.